Transcript lesson 5.7 Curve Fit..

6 minutes
Warm-Up
1) Write the system of equations represented by
2 2  x   16 
 1 3  y    4 

   
2) Write the matrix equation that represents
x  y  6

2x  4
3) Find the inverse of
 3 1 
 4 2


5.7 Curve Fitting With Quadratic Models
Objectives:
•Find a quadratic function that exactly fits three data
points
•Find a quadratic model to represent a data set
Example 1
Find a quadratic equation whose graph contains the
points (-3,16), (2,6), and (1,-4).
Step 1: Write a system of equations in three variables
y = ax2 + bx + c
Point
Substitution
Equation
(-3,16)
a(-3)2 + b(-3) + c = 16
9a – 3b + c = 16
(2,6)
a(2)2 + b(2) + c = 6
4a + 2b + c = 6
(1,-4)
a(1)2 + b(1) + c = -4
a + b + c = -4
Step 2: Use a matrix equation to solve the system
 9 3 1  a   16 
 4 2 1 b    6 

   
 1 1 1  c   4 
Example 1
Find a quadratic equation whose graph contains the
points (-3,16), (2,6), and (1,-4).
Step 2: Use a matrix equation to solve the system
 9 3 1  a   16 
 4 2 1 b    6 

   
 1 1 1  c   4 
Step 3: Write the quadratic equation
Example 2
Find a quadratic model to represent the data in the
table below.
Step 1: Enter the data and make a scatter plot
Step 2: Use the quadratic regression
feature to find a quadratic model
y = 0.008x2 + 0.518x + 131.886
x
y
25
50
150
178
75
100
216
265
125
150
175
323
392
470.4
Homework
workbooks p.33 #1,7,13-17